Order-4 apeirogonal tiling


In geometry, the order-4 apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of.

Symmetry

This tiling represents the mirror lines of *2∞ symmetry. It dual to this tiling represents the fundamental domains of orbifold notation *∞∞∞∞ symmetry, a square domain with four ideal vertices.

Uniform colorings

Like the Euclidean square tiling there are 9 uniform colorings for this tiling, with 3 uniform colorings generated by triangle reflective domains. A fourth can be constructed from an infinite square symmetry with 4 colors around a vertex. The checker board, r, coloring defines the fundamental domains of , symmetry, usually shown as black and white domains of reflective orientations.

Related polyhedra and tiling

This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with four faces per vertex, starting with the octahedron, with Schläfli symbol, and Coxeter diagram, with n progressing to infinity.